`pi(int_0^(pi/2)((1 + cos(x))^2 - 1^2)dx)` Each integral represents the volume of a solid. Describe the solid.

The formula provided represents the volume of the solid obtained by rotating the region enclosed by the curves `y = 1 + cosx, y = 1, x = 0, x = pi/2` , about y axis, using washer method:

`V = pi*int_a^b (f^2(x) - g^2(x))dx, f(x)>g(x)`

You need to find the endpoints by solving the equation:

`1 + cosx = 1 => cos x = 0 => x=-pi/2, x = pi/2`

`V = pi*int_0^(pi/2) (1 + cosx )^2 - 1^2)dx`

`V = pi*int_0^(pi/2) (1 + 2cos x + cos^2 x - 1)dx`

`V = pi*int_0^(pi/2) (2cos x + cos^2 x)dx`

`V = pi*(int_0^(pi/2) (2cos x) dx + int_0^(pi/2) (cos^2 x)dx)`

`V = pi*(2 sin x + int_0^(pi/2) (1+cos 2x)/2 dx)`

`V = pi*(2 sin x + x/2 + (sin2x)/4)|_0^(pi/2)`

`V = pi*(2sin(pi/2) + pi/4 + 0 - 2*0 - 0/2 - 0/4)`

`V = pi*(2 + pi/4)`

`V = (pi*(8+pi))/4`

Hence, evaluating the volume of the solid obtained by rotating the region enclosed by the curves `y = 1 + cosx, y = 1, x = 0, x = pi/2, ` about y axis, using washer method, yields `V = (pi*(8+pi))/4.`